FutureStepsSign in 6th grade learning.
Make the idea click.
Sixth-grade learning introduces more comparisons, models and independent explanations. Use a unit-rate example to see how a common basis can make two options easier to compare.
Try the worked exampleCompare like with like
A cheaper pack is not always cheaper per item. Divide the total price by the number of identical items, label the rate, and compare the results. In other subjects, pause to ask whether two figures or sources describe the same thing before drawing a conclusion.
What does one unit mean in this question?
Explore 6th grade subjects.
Mathematics
Selected starter topics
Reason about rational numbers, percents, equivalent expressions, area, coordinates and data using worked examples.
- Opposites and distance from zero
- Compare rates using one unit
- Undo one operation to solve an equation
English language arts
Selected starter topics
Use original passages to explore vocabulary, themes, poetry, drama, arguments, sentence craft and responsible research.
- Support an inference with connected clues
- Find the turning point in a plot
- How much does the narrator know?
Science
Selected starter topics
Use evidence to explain mixtures, density, forces, energy, seasons, rocks, cells and ecosystems.
- Explain matter with moving particles
- A force pair acts on two objects
- Living things depend on shared resources
Social studies
Selected starter topics
Explore world connections, geography, economic indicators, government, culture and evidence-based community choices.
- Locate places with latitude and longitude
- Adapt to or modify an environment
- How resources connect places through trade
These examples come from FutureSteps’ Texas starter collection. They introduce selected topics and support review; they are not a complete curriculum, school assessment or course credit.
Compare rates using one unit
Use equivalent rates to compare quantities measured in different-sized groups.
A rate compares quantities with different units, such as dollars and notebooks. A unit rate tells you the amount for one unit. It makes groups of different sizes easier to compare fairly.
Divide both quantities by the same number to keep the rate equivalent. Always include the units: dollars per notebook and notebooks per dollar answer different questions.
One pack has 3 identical notebooks for $6. Another has 5 for $15. Which costs less per notebook?
- For the first pack, divide $6 by 3 notebooks to get $2 per notebook. This spreads the price equally across the three items.
- For the second pack, divide $15 by 5 notebooks to get $3 per notebook. Now both prices refer to one notebook.
- Compare $2 with $3. The first pack costs less per notebook; comparing $6 with $15 alone would ignore that the packs have different sizes.
Your turn.
A pack of 4 identical pens costs $10. What is the cost per pen?
- $0.40 per pen
- $6 per pen
- $2.50 per pen
Show the answer and explanation
$2.50 per pen
$10 ÷ 4 pens = $2.50 per pen. Check by multiplying $2.50 × 4 = $10.
Example from the FutureSteps Mathematics starter collection. Course reference: Texas TEKS · Grade 6 Mathematics. The example is app-authored; the reference does not imply endorsement or complete coverage.
A routine to try next.
- Write down the quantities and their units before choosing an operation.
- Convert each comparison to the same basis, such as cost per notebook.
- Explain the decision in words and identify any assumption, such as identical item quality.
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Questions before you begin.
Is every sixth grader eligible for an account?
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